How about cork?

Going straight from one color to another between rooms can potentially look too much like a patchwork quilt. Homeowners often throw a third material (tile, stone) in between the two floor materials to make a more seamless transition. Hope that helps!

Your photo suggests that your existing flooring is a basic solid red oak strip floor.
Looks like a more "southern" variety (because of the coloration).
If it's 2-1/4" wide, it will be 3/4" thick.
Although it's tough to tell the widths in the pic... a tape measure would do the trick.

Why not have someone (like us, for example) produce the amount of flooring needed to match your existing floor in a custom prefinished format?
Photos attached are NOT red oak, but are for illustration.

Drop us a line at: david@selecthardwoodfloor.com if you have any questions.

Hanna beat me to it. Cork flooring is the closest thing to "carpet" that you can get while still working with a hard surface. Cork will eat up the sound in the rooms as well as reduce the sound entering the space (nice and quiet for bedrooms). For allergies/chemical sensitivities, cork is the number one flooring choice. It is hypo-allergenic, anti-microbial (naturally) and is a low-static surface (dust is not attracted to it).

Be careful of floors that advertise "Microban". Microban is a chemical additive that is a hormone disruptor = female changes to male bodies. This has been banned in Europe and Japan...the USA has started looking into the health claims and Canada can't seem to see what the fuss is all about.

Forna cork floors are built to European standards = no added chemicals = very low VOC rating by the EU. Just a thought.

Thanks for the info, Cancork. :)